Courses: 4th Year 1st Sem., B. Sc. Mathematics

MTH411: Theory of Ordinary Differential Equations
(3 credit units)The general first order equation, Existence and uniqueness theorems.Singularpoints.Differentia inequalities. Autonomous systemsorbits, limits and invariants sets. Linearisation.Stability, liapunovtheory.Green’sfunction.Periodicsolution.Special topics.

MTH421: Applied Functional Analysis I
(3 credit units)Metric spaces and fixed points; metric spaces optimal economic growth problems, fixed points by successive approximations, applications of contraction mapping principle. Integration theory: fundamental result: the integration in S1, closure of S1and S2, complete spaces of integrable functions.

MTH431: Lebesgue Measure and Integration
(3 credit units)Lebesgue measure; measurable and nonmeasurable sets. Measurable functions. Lebesgue integral; integration of nonnegative functions the general int5egral convergence theorem.

MTH441: Mathematical Methods II
(3 credit units)Calculus of variation: Lagrange’s functional and associated density. Necessary condition for a weak relative extremum.Hamilton’sprinciples.Lagrange’s equations and geodesic problems.The du Bois Raymond equation and corner conditions.Variable endpoints and related theorems. Sufficient conditions for a minimum. Isoperimetric problems.Variational integral transforms. Lap lace, Fourier and Hankel transforms. Complex variable methods.Convolutiontheorems.Application to solution of differential equations.

MTH451: History of Mathematics
(2 credit units)The origin of Mathematics historical relations between geometry and algebra.The origin and development of calculus and analysis.Euclidean and non Euclidean geometry. The development of algebra, groups.

GST311: Introduction to Entrepreneurial Studies
(2 credit units)Some of the ventures to be focused upon include the following: soap/detergent, tooth brushes and tooth paste making; photography; brick, nails, screws making; dyeing/textile blocks paste making; rope making; plumbing; vulcanizing; brewing; glassware production/ceramic production; paper production; water treatment/conditioning/packaging; food processing/packaging/preservation; metal working/fabricationsteel and aluminum door and windows; training industry; vegetable oil /and salt extractions; fisheries/aquaculture; refrigeration/air conditioning; plastic making; farming (crop); domestic electrical wiring; radio/TV repairs; carving; weaving; brick laying/making; bakery; tailoring; iron welding; building drawing; carpentry; leather tanning; interior decoration; printing; animal husbandry (poultry, piggery, goat.); metal craftblacksmith, tinsmith; sanitary wares; vehicles maintenance and bookkeeping.

MTH401: Seminar
(1 credit units) 
MTH481: Analytical Dynamics II
(3 credit units)Lagrange’s equations for nonhomonymic systems. Lagrange multiplies. Variational principles; calculus of variation, Hamilton’s principle.Lagrange’s equations from Hamilton’s principles.Canonicaltransformations.Normal modes of vibrations.HamiltonJacobin equations.Euler’s angles.

MTH491: Fluid Mechanics
(3 credit units)Real and Ideal fluids.Differentiation following the motion of fluid particles.Equations of motion and continuity for incompressible invscid fluids. Velocity potentials and stoke’s stream functions. Bernoulli’s equation with application to flow along curve4d paths.Kineticenergy.Sources, sinks, doubles in 2 and 3 dimensions, limiting streamlines.Images and rigid planes.KuttaJoukowski’stheorem.Vortices, circulation, Blassius Theorem, Irrotational flow.

MTH461: Numerical Analysis II
(3 credit units)The basic Gaussian Elimination Methods. Gaussian Elimination methods with partial pivoting.Algorithms for both basic G.E.M. and G.E.M. with partial pivoting. Inner products and Gram Schmidt process. Matrix and Vector Norms. Error Analysis of Linear Systems.The condition number of a matrix. Iterative Methods for Linear equations such as: Jacobi method, GaussSeidel Method. Convergence analysis of Iterative methods.Linear systems arising from partial differential equations.The finite difference methods.Solution of elliptic, parabolic and hyperbolic equations by finite difference methods.

MTH471: Complex Analysis II
(3 credit units)Laurent expansions.Isolated singularities and residues.Residue theorem calculus of residue, and application to evaluation of integrals and to summation of series.Maximum modulus principle.Argumentprinciple.Ruche’stheorem.The fundamental theorem of algebra.Principle of analytic continuation.Multiple valued functions and Riemann surfaces.
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